Learn on PengiBig Ideas Math, Course 1Chapter 3: Algebraic Expressions and Properties

Lesson 2: Writing Expressions

In this Grade 6 lesson from Big Ideas Math, Course 1 (Chapter 3), students learn how to write numerical and algebraic expressions to represent unknown quantities using variables. They practice identifying key words and phrases that signal the four operations, such as "more than" for addition, "fewer than" for subtraction, "product of" for multiplication, and "quotient of" for division. The lesson aligns with Common Core standard 6.EE.2a and builds skills in translating real-world phrases into expressions like x + 14 or 3 ÷ z.

Section 1

Translating Words into Expressions

Property

To translate a word problem into an algebraic expression, start by identifying an unknown and use a variable to represent it.
Next, identify what you do know (the given numbers).
Finally, determine what connects the two pieces of information together to write an algebraic expression that represents the situation.

Examples

Section 2

Keywords for Translating Phrases

Property

Translating word phrases into algebraic expressions involves identifying keywords that signify mathematical operations.

  • Addition: sum, more than, plus, increased by
  • Subtraction: difference, less than, minus, decreased by
  • Multiplication: product, times, twice
  • Division: quotient, divided by

Examples

  • Translate "the product of 4 and a number x" into an expression. The keyword "product" means multiplication, so the expression is 4x4x.

Section 3

Writing Expressions from Verbal Phrases

Property

To translate verbal phrases that group quantities, use parentheses ()(). Phrases like "the sum of..." or "the difference between..." that are then multiplied or divided require parentheses to ensure the addition or subtraction is performed first. For example, "the sum of aa and bb, times cc" is written as (a+b)×c(a + b) \times c.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Translating Words into Expressions

Property

To translate a word problem into an algebraic expression, start by identifying an unknown and use a variable to represent it.
Next, identify what you do know (the given numbers).
Finally, determine what connects the two pieces of information together to write an algebraic expression that represents the situation.

Examples

Section 2

Keywords for Translating Phrases

Property

Translating word phrases into algebraic expressions involves identifying keywords that signify mathematical operations.

  • Addition: sum, more than, plus, increased by
  • Subtraction: difference, less than, minus, decreased by
  • Multiplication: product, times, twice
  • Division: quotient, divided by

Examples

  • Translate "the product of 4 and a number x" into an expression. The keyword "product" means multiplication, so the expression is 4x4x.

Section 3

Writing Expressions from Verbal Phrases

Property

To translate verbal phrases that group quantities, use parentheses ()(). Phrases like "the sum of..." or "the difference between..." that are then multiplied or divided require parentheses to ensure the addition or subtraction is performed first. For example, "the sum of aa and bb, times cc" is written as (a+b)×c(a + b) \times c.

Examples